Best Known (174, s)-Sequences in Base 3
(174, 96)-Sequence over F3 — Constructive and digital
Digital (174, 96)-sequence over F3, using
- Niederreiter–Xing sequence construction III based on function field F4/F3 with g(F4) = 79, N(F4) ≥ 2, and N(F4) + N2(F4) ≥ 97 from GarcÃa–Stichtenoth tower as constant field extension [i]
(174, 162)-Sequence over F3 — Digital
Digital (174, 162)-sequence over F3, using
- t-expansion [i] based on digital (151, 162)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 151 and N(F) ≥ 163, using
(174, 361)-Sequence in Base 3 — Upper bound on s
There is no (174, 362)-sequence in base 3, because
- net from sequence [i] would yield (174, m, 363)-net in base 3 for arbitrarily large m, but
- m-reduction [i] would yield (174, 1808, 363)-net in base 3, but
- extracting embedded OOA [i] would yield OOA(31808, 363, S3, 5, 1634), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 23 702866 888774 242868 393456 267782 237295 263586 569797 607577 988929 795465 599989 503631 257481 474440 138697 426445 062621 488026 959504 957523 479430 319106 496596 105668 128698 119074 781133 306685 267805 717327 439899 483086 842657 054953 773561 316973 223132 272846 238509 149193 033439 343178 198155 954399 473883 435995 978289 478221 452667 580136 229680 487701 669284 759617 472624 804736 760951 069944 216658 499546 398548 736936 625096 841814 166268 446703 937666 490244 201168 696655 712733 018272 425491 819865 976702 443051 703050 651987 451172 426488 553180 865555 566654 704456 921231 578325 597421 896348 243591 709533 354587 856710 730200 771019 398151 458863 639966 457500 439260 316582 782332 796199 697164 173714 494604 399426 113489 759694 580853 314324 158578 371872 722050 065991 912266 860064 873818 604455 370072 010106 004676 418441 301812 471575 003717 635958 893899 501560 625591 722339 886736 477122 305066 613230 816721 408257 512945 553964 761236 877442 050788 980534 245989 / 545 > 31808 [i]
- extracting embedded OOA [i] would yield OOA(31808, 363, S3, 5, 1634), but
- m-reduction [i] would yield (174, 1808, 363)-net in base 3, but